Question

Can someone PLEASE explain to me how the integral of 2cos^2(t)sin(t) dt =-(2/3)cos^3(t) ???

Answer 1

Do the change of variable
`u=\cos(t)\rightarrow du=-\sin(t)dt`

Then
`\int\2cos^2(t)\sin(t)dt=-2\int u^2du=-\frac{u^3}3=-\frac{2}3\cos^3(t)`